Chapter 12 6
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Chapter 12.6. Surface Area and Volume of Spheres. Concept. Surface Area of a Sphere. Example 1. Find the surface area of the sphere. Round to the nearest tenth. S =4  r 2 Surface area of a sphere =4 (4.5) 2 Replace r with 4.5. ≈254.5Simplify. Answer: 254.5 in 2.

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Chapter 12.6

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Chapter 12 6

Chapter 12.6

Surface Area and Volume of Spheres


Concept

Concept


Example 1

Surface Area of a Sphere

Example 1

Find the surface area of the sphere. Round to the nearest tenth.

S=4r2Surface area of a sphere

=4(4.5)2Replace r with 4.5.

≈254.5Simplify.

Answer:254.5 in2


Example 11

Example 1

Find the surface area of the sphere. Round to the nearest tenth.

A.462.7 in2

B.473.1 in2

C.482.6 in2

D.490.9 in2


Example 2a

Use Great Circles to Find Surface Area

Example 2A

A. Find the surface area of the hemisphere.

Find half the area of a sphere with the radius of 3.7 millimeters. Then add the area of the great circle.


Example 2b

Use Great Circles to Find Surface Area

Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 10 feet.

First, find the radius. The circumference of a great circle is 2r. So, 2r = 10 or r = 5.


Example 2c

Use Great Circles to Find Surface Area

Example 2C

C. Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.

First, find the radius. The area of a great circle is r2. So, r2 = 220 or r≈ 8.4.


Example 2a1

Example 2A

A. Find the surface area of the hemisphere.

A.110.8 m2

B.166.3 m2

C.169.5 m2

D.172.8 m2


Example 2b1

Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 8 feet.

A.100.5 ft2

B.201.1 ft2

C.402.2 ft2

D.804.3 ft2


Example 2c1

Example 2C

C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters.

A.320 ft2

B.440 ft2

C.640 ft2

D.720 ft2


Concept1

Concept


Example 3a

(15)3r = 15

Volumes of Spheres and Hemispheres

Example 3A

A. Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth.

Find the radius of the sphere. The circumference of a great circle is 2r. So, 2r = 30 or r = 15.

≈ 14,137.2 cm3


Example 3b

r 3

Use a calculator.

Volumes of Spheres and Hemispheres

Example 3B

B. Find the volume of the hemisphere with a diameter of 6 feet. Round to the nearest tenth.

The volume of a hemisphere is one-half the volume of the sphere.

Volume of a hemisphere

Answer: The volume of the hemisphere is approximately 56.5 cubic feet.


Example 3a1

Example 3A

A. Find the volume of the sphere to the nearest tenth.

A.268.1 cm3

B.1608.5 cm3

C.2144.7 cm3

D.6434 cm3


Example 3b1

Example 3B

B. Find the volume of the hemisphere to the nearest tenth.

A.3351.0 m3

B.6702.1 m3

C.268,082.6 m3

D.134,041.3 m3


Example 4

Solve Problems Involving Solids

Example 4

ARCHEOLOGYThe stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere?

UnderstandYou know that the volume of the stoneis 36,000 cubic inches.

PlanFirst use the volume formula to find theradius. Then find the diameter.


Example 41

Example 4

RECESS The jungle gym outside of Jada’s school is a perfect hemisphere. It has a volume of 4,000 cubic feet. What is the diameter of the jungle gym?

A.10.7 feet

B.12.6 feet

C.14.4 feet

D.36.3 feet


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